Solution 1:

Verbs often take Direct Objects. Nouns never do. Instead, the semantically comparable string must appear within a preposition phrase, usually one using the preposition of:

  • they massacre [the civilians] (verb massacre taking direct object)
  • the massacre [of the civilians] (noun massacre taking an of preposition phrase)

Verbs can be premodified by adverbs. Nouns never can. Nouns can be premodified by adjectives. Verbs never can:

  • the gentle sway
  • *the gently sway (adverb premodifying noun - ungrammatical)
  • gently swayed
  • *gentle swayed (adjective premodifying verb - ungrammatical)

The Original Poster's example

The White House website, without naming China, promises to ...

Here we see China appearing as the Direct Object of the verb naming. Notice that we cannot put China within an of-preposition phrase here:

  • *The White House website, without naming of China, promises to ... (ungrammatical)

We can further see that if we want to premodify the word naming we must use an adverb. We cannot use an adjective:

  • without directly naming China (adverb directly)
  • *without direct naming China (adjective direct - ungrammatical)

This data shows that the word naming is a verb in the Original Poster's example, not an adjective.